|MadSci Network: Medicine|
Well tatoos aren't permanent. There are several (costly and painfull) ways to get rid of them. They involve plastic surgery (just cutting it away ;) and sessions of special laser treatment.
However, to respond to your question. The human body does not(!) replace all it cells constantly. Actually most cells are just in a non-dividing state. The best example are the braincells, but many other cells also don't divide. The upper cell layer of the skin is however an area which is constantly dividing and replacing lost cells. This layer is quite thin. Just a few living cells thick.
Below this layer of often dividing cells there is supportive tissue which doesn't divide much in adult people. This is the layer in which the pigment (color) is injected.
Hope this helps,
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